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Diagnostic for the Decay Ring : Energy Monitoring

Diagnostic for the Decay Ring : Energy Monitoring. m. apollonio – Imperial College London. the lattice of the DK racetrack ring G4beamline 3D model the method of spin depolarisation resolution in ideal case detector issues (location, …) conclusions.

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Diagnostic for the Decay Ring : Energy Monitoring

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  1. Diagnostic for the Decay Ring : Energy Monitoring m. apollonio – Imperial College London UKNF - Imperial College London

  2. the lattice of the DK racetrack ring • G4beamline 3D model • the method of spin depolarisation • resolution in ideal case • detector issues (location, …) • conclusions UKNF - Imperial College London

  3. lattice g4beamline model spin depolarisation ideal case detector issues conclusions Track DK Ring lattice [C. Prior, IDS baseline] Pm= 25 GeV/c eN = 4.8 mm rad e = 0.02 mm rad aN = 30 mm rad (accept) a= 0.127 mm rad Twiss Parameters (MADX) straights: sx = 51 mm sx’ = 0.4 mrad arcs: sx = 16 mm sx’ = 0.13 mrad 1/g = 4 mrad sx’ * g ~ 0.1 UKNF - Imperial College London

  4. straight section matching section arc section lattice g4beamline model spin depolarisation ideal case detector issues conclusions G4beamline MODEL main open issues on diagnostics - measurement of divergence - measurement beam current - measurement of energy via beam (de)polarisation location for the device? UKNF - Imperial College London

  5. lattice g4beamline model spin depolarisation ideal case detector issues conclusions UKNF - Imperial College London

  6. lattice g4beamline model spin depolarisation ideal case detector issues conclusions • Energy can be measured using the Polarisation of the Muon Beam • [ Raja-Tollestrup – FERMILAB-Pub-97 / 402] IF some P is saved after • all the massage in the machines ... • I assume P= 27% is left when filling the DK ring • Spin precesses in a ring due to coupling with magnetic fields • (bending magnets). NB: the trick does NOT work in a bow-tie shape • At every turn spin precession is determined by the SPIN TUNE: • w = 2 p g a • a = 1.16E-3 • This determines a modulation in P • NB: if DE/E =0  g same for all muons  P keeps oscillating • if DE/E !=0  P goes to 0 after n turns • e+ spectrum from m-decay is a function of P: • d2N/dx dcosq = N0[(3-2x)x2 – P(1-x)x2 cosq] (CM) • I have modelled the behaviour of a beam made of 100000 muons, all with their spin and energy (DE/E =[0.01-0.05]) • Lorentz Boost • Modulation in P produces a modulation in E(e+) turn0 turn1 turn2 Sz(1) Sz(0) Sz(2) UKNF - Imperial College London

  7. lattice g4beamline model spin depolarisation ideal case detector issues conclusions Centre of Mass frame: P=+100% x=2Ee/mm Pe cosq LAB frameafter Lorentz boost Cos (qLAB) X=2Ee/mm (CM) Pe LAB cosqLAB ~ 1 0.99996 UKNF - Imperial College London E (MeV)

  8. lattice g4beamline model spin depolarisation ideal case detector issues conclusions DP/P = 3% Pol=27% fine mesh = 10 samples / turn TURN POL (%) P modulation (spin precession) and damping (DE/E !=0) turn # UKNF - Imperial College London

  9. lattice g4beamline model spin depolarisation ideal case detector issues conclusions • MEASURABLE SIGNAL • collect electrons at three different energy bins • [0,5] GeV • [5,10] GeV • [10,25] GeV • measure the TOTAL energy deposited • (e.g. in a calorimeter) • Energy resolution modeled as: sE/E=SQRT(1.03…/Ne) • [Raja-Tollestrup] • obtain a signal which shows: • an oscillation due to Polarisation • a decay slope due to continuous muon decays • a modulation/damping due to DE/E • fit the signal at every TURN with a function: • f(T) = A e-BT (C exp-(G T2) cos(D+E T) + F) • G: contains DP/P • E: is the SPIN tune from which g can be inferred • B: describes muon decay slope UKNF - Imperial College London

  10. lattice g4beamline model spin depolarisation ideal case detector issues conclusions 31% in [0,5] GeV/c Ee (GeV) 100000 initial muon decays turn # UKNF - Imperial College London

  11. lattice g4beamline model spin depolarisation ideal case detector issues conclusions 28% in [5,10] GeV/c UKNF - Imperial College London

  12. lattice g4beamline model spin depolarisation ideal case detector issues conclusions 41% in [10,25] GeV/c UKNF - Imperial College London

  13. lattice g4beamline model spin depolarisation ideal casedetector issues conclusions This is somewhat ideal ... we need to collect the electrons! How do we turn it into a realistic device for our case? It has been suggested [Blondel – ECFA 99-197(1999)] to use the first bending magnet after the decay straight section to SELECT electron energy bins: what does that mean today with a realistic lattice (25 GeV)? In fact electron is emitted ~parallel to m (due to the high g) The spectral power of the 1st magnet depends on its FIELD and LENGTH A G4Beamline simulation can tell us where electrons impinge after decaying somewhere along the orbit UKNF - Imperial College London

  14. lattice g4beamline model spin depolarisation ideal case detector issues conclusions use a “realistic” beam of m+ from Zgoubi [C. Prior]- Pm = 25 GeV/c DP/P = 1% - eN = 30 mm rad m at mid - straight m at end of straight UKNF - Imperial College London

  15. latticeg4beamline model spin depolarisation ideal case detector issues conclusions elmon5 elmon4 elmon3 elmon2 elmon1 e from m decays … B2 B= -4.27T/L=2.0m B1 B= -4.27T/L=2.0m M3 B=+0.35T/L=2.3m M2 B=-1.9T/L=0.6m M1 B=-0.64T /L=4.0m m beam force m decay UKNF - Imperial College London

  16. latticeg4beamline model spin depolarisation ideal case detector issues conclusions First Dipole of the matching section B= -0.64T / L=4.0m First Dipole of the Arc section B= -4.27T / L=2.0m elmon2 elmon1 low P e- elmon5 elmon4 force m decay UKNF - Imperial College London

  17. latticeg4beamline model spin depolarisation ideal case detector issues conclusions elmon5 sensible plane UKNF - Imperial College London

  18. latticeg4beamline model spin depolarisation ideal case detector issues conclusions latticeg4beamline model spin depolarisation ideal case detector issues conclusions elmon4 sensible plane magnet gap Dipole Length = 2m UKNF - Imperial College London

  19. latticeg4beamline model spin depolarisation ideal case detector issues conclusions elmon3 long drift for higher momenta drift path ~ 13 m force m decay UKNF - Imperial College London

  20. e+ out of the aperture latticeg4beamline model spin depolarisation ideal case detector issues conclusions Elmon3 – DS of M2  consider Ee = [2.5-7.5] UKNF - Imperial College London

  21. lattice g4beamline model spin depolarisationideal case detector issues conclusions How does TOT Ee changes turn by turn? OUT OF detector acceptance TOT Ee in [12.5,25] GeV/c bin fit on 40 turns TOT Ee in [12.5,25] GeV/c bin fit on 80 turns TOT Ee in [2.5,7.5] GeV/c bin fit on 40 turns TOT Ee in [2.5,7.5] GeV/c bin fit on 80 turns UKNF - Imperial College London

  22. lattice g4beamline model spin depolarisation ideal case detector issues conclusions consider an initial sample of ~100000 e- [0,25]bin [2.5,7.5] = 30% measure E (DE/E) with (de)polarisation after n turnE = 25009+/-44 after 40 turns (24986+/-23, 100 turns)DE/E = 0.89+/-0.36 after 40 turns (0.93+/-0.07, 100 turns)Q.: how many electrons can I collect at turn=0? OUT OF detector acceptance [12.5,25] GeV/c – DE/E [12.5,25] GeV/c – Energy Bias = (E-25)/25 [2.5,7.5] GeV/c – Energy Bias [2.5,7.5] GeV/c – DE/E UKNF - Imperial College London

  23. 2ns 88 B 3ns lattice g4beamline model spin depolarisation ideal case detector issues conclusions 1021n/yr (1yr = 200 days) = 5.8x1013n/s • 50 Hz (proton) rep. rate = 20 ms (fill)  • 1.16 x 1012n per fill • NB: every fill = 3 bunch trains (L=440ns / S=1200ns) • how many e+ (say) in a 10m section before the bending element? • 10/1608 * 1.16 * 1012 = 7*109 • 30%[2.5-7.5GeV/c] 2*109 (T) (S) 440ns 1200ns 1640ns Tperiod = 5.36 msec tm=520 msec 2x104msec = 50Hz rep.rate UKNF - Imperial College London

  24. latticeg4beamline model spin depolarisation ideal case detector issues conclusions Open issues: - which electrons are relevant for the measurement? i.e. which decay pointsupstream of the bending dipole? - 1m? 10m? 100m upstream? ideal decay point decay region >10m B A UKNF - Imperial College London

  25. latticeg4beamline model spin depolarisation ideal case detector issues conclusions to do list:a- introduce polarisation(*) of the beam  Zgoubib- use Zgoubi-generated files as input for G4beamlinec- force the decay over a continuous volume (length) = some technicalities with g4bl to be solvedd- build the e+spectrum at elmon(i)e- perform fit and evaluate precision/biases (*) so far a self made model UKNF - Imperial College London

  26. lattice g4beamline model spin depolarisation ideal case detector issues conclusions Conclusions • method of Energy Monitoring via depolarisation revived for the IDS Race Track Decay Ring • Use of G4Beamline for a more realistic rendering of the events • Zgoubi to realistically describe P • detailed study on how distributed decays (upstream of a dipole) change an e+ spectrum • think of a better geometry/technology for a possible detector • evaluate e+ rate in interested areas UKNF - Imperial College London

  27. latticeg4beamline model spin depolarisation ideal case detector issues conclusions to do list: a- force the decay over a continuous volume (length) = some technicalities with g4bl to be solvedb- build the e+spectrum at elmon(i)c- introduce polarisation (verify if P is taken into account in g4bl)d- perform fit and evaluate precision/biases UKNF - Imperial College London

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